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Differential Forms and Applications

Differential Forms and Applications - 94 edition

ISBN13: 978-3540576181

Cover of Differential Forms and Applications 94 (ISBN 978-3540576181)
ISBN13: 978-3540576181
ISBN10: 3540576185
Cover type:
Edition/Copyright: 94
Publisher: Springer-Verlag New York
Published: 1994
International: No

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Differential Forms and Applications - 94 edition

ISBN13: 978-3540576181

Manfredo P. Docarmo

ISBN13: 978-3540576181
ISBN10: 3540576185
Cover type:
Edition/Copyright: 94
Publisher: Springer-Verlag New York

Published: 1994
International: No
Summary

The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely the Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames of E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. Everything is then put together in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Table of Contents

Preface
1. Differential Forms in Rn
2. Line Integrals
3. Differentiable Manifolds
4. Integration on Manifolds; Stokes Theorem and Poincaré's Lemma
5. Differential Geometry of Surfaces
Th Theorem of Gauss-Bonnet and the Theorem of Morse
References
Index

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